A modified expression for the Hamiltonian expectation value exploiting the short-range behavior of the wave function

TL;DR

This paper introduces a modified Hamiltonian expectation value formula that better accounts for short-range electron interactions, improving energy estimates for electronic systems.

Contribution

It presents a new scaling approach for the Hamiltonian expectation value that incorporates short-range behavior, enhancing accuracy over traditional models.

Findings

Improved energy estimates for Harmonium ground and excited states.

Significant reduction in error compared to standard models.

Applicable to systems with two to six electrons.

Abstract

The expectation value of the Hamiltonian using a model wave function is widely used to estimate the eigenvalues of electronic Hamiltonians. We explore here a modified formula for models based on long-range interaction. It scales differently the singlet and triplet component of the repulsion between electrons not present in the model (its short-range part). The scaling factors depend uniquely on the parameter used in defining the model interaction, and are constructed using only exact properties. We show results for the ground states and low-lying excited states of Harmonium with two to six electrons. We obtain important improvements for the estimation of the exact energy, not only over the model energy, but also over the expectation value of the Hamiltonian.